ABSTRACT
Consider any random experiment where subjects are classified into one of two mutually exclusive categories. For example, subjects might either pass or fail a statistics course, survive or die after an operation, exhibit signs of schizophrenia or have no signs, etc. For these situations, a special probability function arises. Called the binomial probability function, it is one of the most important probability functions for discrete random variables. For a random sample of n subjects, it turns out that there is a simple expression for determining the probability that exactly x subjects will belong to the first category, and the remaining n-x belong to the second. Three goals in this chapter are to derive this expression, indicate some of the properties of the resulting probability function, and to briefly indicate how the probability function can be used. Additional applications are discussed in chapter five. Another goal is to introduce the normal distribution and to discuss some of its properties.
